On the Jacquet Conjecture on the local converse problem for 𝑝-adic 𝐺𝐿_{𝑁}

Adrian, Moshe; Liu, Baiying; Stevens, Shaun; Xu, Peng

doi:10.1090/ert/476

On the Jacquet Conjecture on the local converse problem for $p$-adic $\mathrm {GL}_N$
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by Moshe Adrian, Baiying Liu, Shaun Stevens and Peng Xu

Represent. Theory 20 (2016), 1-13

DOI: https://doi.org/10.1090/ert/476

Published electronically: January 27, 2016

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Abstract:

Based on previous results of Jiang, Nien and the third-named author, we prove that any two minimax unitarizable supercuspidals of $p$-adic $\mathrm {GL}_N$ that have the same depth and central character admit a special pair of Whittaker functions. As a corollary of our result, we prove Jacquet’s conjecture on the local converse problem for $\mathrm {GL}_N$, when $N$ is prime.

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